Kinetic surface roughening for the Mullins–Herring equation

Using the linearity property of the Mullins–Herring equation when the velocity is zero with a Gaussian noise, we obtain an analytic form for the global mean square surface width and height-height correlation function. This can be used to read the critical exponents in any dimension. In particular, for d=1 we show that although the surface is super rough, the system exhibits Family–Vicsek scaling behavior.